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Practice Exam 1: MAP 4305
*
1. Does
xy
′′
+ (
x
+ 2)
y
′

y
= 0
, x >
0
,
have a solution which is bounded near zero? Notice that to answer this question, you only need to
consider the indicial equation.
2. Determine the form of a series expansion about
x
= 0 of 2 linearly independent solutions to:
x
2
y
′′

xy
′
+ (1

x
2
)
y
= 0
, x >
0
.
Do not Fnd a recursion formula for the coe±cients.
3. Let
J
ν
(
x
) be the Bessel function of the Frst kind of order
ν
≥
0:
J
ν
(
x
) =
∞
s
n
=0
(

1)
n
n
!Γ(1 +
ν
+
n
)
p
x
2
P
2
n
+
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This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.
 Summer '06
 DeLeenheer

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